Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nystr\"om approximation. After reviewing and contrasting a number of hyperparameter tuning strategies, we propose a complexity regularization criterion based on a data dependent penalty, and discuss its efficient optimization. Then, we proceed to a careful and extensive empirical evaluation highlighting strengths and weaknesses of the different tuning strategies. Our analysis shows the benefit of the proposed approach, that we hence incorporate in a library for large scale kernel methods to derive adaptively tuned solutions.

翻译：内核方法为非参数学习提供了一种原则性的方法。虽然它们的基本实施范围不及大型问题,但最近的进展显示,近似溶解器能够有效地处理大量数据集。这些解决办法的一个缺点是超参数调试没有得到注意,而是留待用户执行。超参数调试在实际中至关重要,缺乏自动调试极大地妨碍了效率和可用性。在本文件中,我们努力填补这一空白,侧重于基于Nystr\"om近似值的内核脊回归。在审查和对比一些超参数调控战略之后,我们提出一个基于数据依赖罚款的复杂规范化标准,并讨论其高效优化。然后,我们着手进行认真和广泛的实验性评估,突出不同调控战略的长处和短处。我们的分析显示了拟议方法的好处,因此我们把大规模内核方法纳入一个图书馆,以获得适应性调整的解决方案。